13,160 research outputs found
Graded persistence diagrams and persistence landscapes
We introduce a refinement of the persistence diagram, the graded persistence
diagram. It is the Mobius inversion of the graded rank function, which is
obtained from the rank function using the unary numeral system. Both
persistence diagrams and graded persistence diagrams are integer-valued
functions on the Cartesian plane. Whereas the persistence diagram takes
non-negative values, the graded persistence diagram takes values of 0, 1, or
-1. The sum of the graded persistence diagrams is the persistence diagram. We
show that the positive and negative points in the k-th graded persistence
diagram correspond to the local maxima and minima, respectively, of the k-th
persistence landscape. We prove a stability theorem for graded persistence
diagrams: the 1-Wasserstein distance between k-th graded persistence diagrams
is bounded by twice the 1-Wasserstein distance between the corresponding
persistence diagrams, and this bound is attained. In the other direction, the
1-Wasserstein distance is a lower bound for the sum of the 1-Wasserstein
distances between the k-th graded persistence diagrams. In fact, the
1-Wasserstein distance for graded persistence diagrams is more discriminative
than the 1-Wasserstein distance for the corresponding persistence diagrams.Comment: accepted for publication in Discrete and Computational Geometr
The design and evolution of the beta two-stage-to-orbit horizontal takeoff and landing launch system
The Beta launch system was originally conceived in 1986 as a horizontal takeoff and landing, fully reusable, two-stage-to-orbit, manned launch vehicle to replace the Shuttle. It was to be capable of delivering a 50,000 lb. payload to low polar orbit. The booster propulsion system consisted of JP fueled turbojets and LH fueled ramjets mounted in pods in an over/under arrangement, and a single LOX/LH fueled SSME rocket. The second stage orbiter, which staged at Mach 8, was powered by an SSME rocket. A major goal was to develop a vehicle design consistent with near term technology. The vehicle design was completed with a GLOW of approximately 2,000,000 lbs. All design goals were met. Since then, interest has shifted to the 10,000 lbs. to low polar orbit payload class. The original Beta was down-sized to meet this payload class. The GLOW of the down-sized vehicle was approximately 1,000,000 lbs. The booster was converted to exclusively air-breathing operation. Because the booster depends on conventional air-breathing propulsion only, the staging Mach number was reduced to 5.5. The orbiter remains an SSME rocket-powered stage
REGIONAL GAINS AND LOSSES FOR CONSUMERS AND PRODUCERS FROM CHANGES IN FLUID MILK PRICES
Agribusiness,
Attractive internal wave patterns
This paper gives background information for the fluid dynamics video on
internal wave motion in a trapezoidal tank.Comment: 2 pg, movie at two resolutions _low(Low-resolution) and
_hr(High-resolution
Attractive internal wave patterns
This paper gives background information for the fluid dynamics video on
internal wave motion in a trapezoidal tank.Comment: 2 pg, movie at two resolutions _low(Low-resolution) and
_hr(High-resolution
Observation of Fano-Resonances in Single-Wall Carbon Nanotubes
We have explored the low-temperature linear and non-linear electrical
conductance of metallic carbon nanotubes (CNTs), which were grown by the
chemical-vapor deposition method. The high transparency of the contacts allows
to study these two-terminal devices in the high conductance regime. We observe
the expected four-fold shell pattern together with Kondo physics at
intermediate transparency {G\alt 2e^2/h} and a transition to the open regime
in which the maximum conductance is doubled and bound by . In
the high- regime, at the transition from a quantum dot to a weak link, the
CNT levels are strongly broadened. Nonetheless, sharp resonances appear
superimposed on the background which varies slowly with gate voltage. The
resonances are identified by their lineshape as Fano resonances. The origin of
Fano resonances is discussed along the modelling.Comment: pdf including figures, see:
http://www.unibas.ch/phys-meso/Research/Papers/2004/Fano-CVD-SWNT.pd
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